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Example 9 - Chapter 3 Class 9 - The World of Numbers (Ganita Manjari I)
Last updated at May 11, 2026 by Teachoo
Decimal Expansion of Real Numbers
Class 9
Chapter 3 Class 9 - The World of Numbers (Ganita Manjari I)
- The Human Need to Count
- Exercise Set 3.1
- The Revolution of Śhūnya
- Integers
- Exercise Set 3.2
- Rational Numbers
- Exercise Set 3.3
- Rational Numbers on the Number Line
- Absolute Value of a Rational Number
- Rational Numbers between two Rational numbers
- Exercise Set 3.4
- Irrational Numbers
- Construction of Length √n on Number line
- The Story of Pi (π) and Madhava’s Infinite Series
- Real Numbers & Imaginary Numbers
-
Decimal Expansion of Real Numbers
- Magic of Cyclic Numbers
- Constructing a Square Root Spiral
- Exercise Set 3.5
- End-of-Chapter Exercises
Transcript
Example 9 Convert 2.45(37) ̅ into the form 𝑝/𝑞. Let x = 2.453737….. Since this is a general repeating decimal, so we look at both non-repeating (after decimal points) and repeating digits Here, ‘45’ is non-repeating (2 digits) ‘37’ repeats (2 digit) Since two digits are non-repeating (i.e. after decimal point) Multiplying equation (1) by 102 i.e. 100 100x = 100 × (2.453737…) 100x = 245.3737… Since two digits are repeating Multiplying equation (2) by 102 i.e. 100 100 × 100x = 100 × (245.3737… ) 10,000x = 24,537.3737… Doing (2) – (1) 10,000x – 100x = 24,537.3737… – 245.3737… Since both have same digits after decimal, we can cancel them 9900x = 24,537 – 245 9900x = 24292 x = 24292/9900 x = 𝟔𝟎𝟕𝟑/𝟐𝟒𝟕𝟓 Thus, 2.45(37) ̅ = 𝟔𝟎𝟕𝟑/𝟐𝟒𝟕𝟓
